论文标题
一些3个manifold不变的复发分析
Resurgent Analysis for Some 3-manifold Invariants
论文作者
论文摘要
当$ g _ {\ mathbb {c}}} = sl（2，\ mathbb {c}）$时，我们研究了一些3个manifold不变性的复兴。我们讨论了一个无限的Seifert歧管系列，以统一根源以及$ s^3 $中的圆环结案例。通过复兴分析，我们看到，Abelian Flat连接到分析持续的Chern-Simons分区功能的贡献包含所有非阿布尔平坦连接的信息，因此可以将其视为分析上持续的Chern-Simons理论在3-manifolds $ M_3 $上的完整分区功能。特别是，这直接表明$ s^3 $中的圆环结的同源块是整个$ g = su（2）$分区函数的分析延续，即彩色的琼斯多项式。
We study resurgence for some 3-manifold invariants when $G_{\mathbb{C}}=SL(2, \mathbb{C})$. We discuss the case of an infinite family of Seifert manifolds for general roots of unity and the case of the torus knot complement in $S^3$. Via resurgent analysis, we see that the contribution from the abelian flat connections to the analytically continued Chern-Simons partition function contains the information of all non-abelian flat connections, so it can be regarded as a full partition function of the analytically continued Chern-Simons theory on 3-manifolds $M_3$. In particular, this directly indicates that the homological block for the torus knot complement in $S^3$ is an analytic continuation of the full $G=SU(2)$ partition function, i.e. the colored Jones polynomial.
